Stochastic and deterministic controls on stratigraphic completeness and fidelity

Compilations of sedimentation rates determined across a large range of time spans and different sedimentary environments attest to the discontinuous nature of sedimentation and support the reasoning that hiatuses pervade sedimentary successions at multiple spatial and temporal scales. The relationship between sedimentation rate and time span of observation also emphasises how stratigraphic completeness is a time span-dependent concept. The scaling of stratigraphic completeness with time span alludes to the likely stochastic, and fractal, nature of the stratigraphic record. It also implies that the relationship between stratal thickness and time is inherently non-linear and this has obvious implications for the way we should expect temporal processes to be recorded stratigraphically. Order within the stratigraphic record may arise from deterministic processes in stratigraphy, most notably through astronomically influenced sedimentation. Intuitively, a strongly ordered stratigraphic record due to the presence of cyclicity in sedimentation increases stratigraphic completeness at time spans equal to and longer than the time span of the cyclicity and minimises the non-linearity between stratal thickness and time. Here, geological data and simple modelling are used to support this supposition, but these results also highlight how stochastic variability inherent in depositional processes may sensitise certain successions to missed cycles and incompleteness, even in the presence of strong cyclicity. This stochastic variability has the potential to mask evidence of astronomical forcing of sedimentation. It is also shown how hiatuses affect the ability of a succession to faithfully record temporal processes, and this is true regardless of whether hiatuses are deterministically controlled or random, or indeed whether a succession is considered complete or not. Consequently, stratigraphic completeness and stratigraphic fidelity are not synonymous terms.